Free products of von Neumann algebras
Author:
Wai Mee Ching
Journal:
Trans. Amer. Math. Soc. 178 (1973), 147-163
MSC:
Primary 46L10
DOI:
https://doi.org/10.1090/S0002-9947-1973-0326405-3
MathSciNet review:
0326405
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Abstract | References | Similar Articles | Additional Information
Abstract: A new method of constructing factors of type ${\text {II}_1}$, called free product, is introduced. It is a generalization of the group construction of factors of type ${\text {II}_1}$ when the given group is a free product of two groups. If ${A_1}$ and ${A_2}$ are two von Neumann algebras with separating cyclic trace vectors and ortho-unitary bases, then the free product ${A_1} \ast {A_2}$ of ${A_1}$ and ${A_2}$ is a factor of type ${\text {II}_1}$ without property $\Gamma$.
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H. Behncke, Automorphisms of $\mathcal {A}({\Phi _2})$, notes.
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Additional Information
Keywords:
von Neumann algebra,
group construction factor of type <!– MATH ${\text {II}_1}$ –> <IMG WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\text {II}_1}$">,
free product,
property <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img10.gif" ALT="$\Gamma$">
Article copyright:
© Copyright 1973
American Mathematical Society